Answer :
Centripetal force needed to keep the 2 kg sack of flour (a) in a circle of radius 4 meters is 8 N and (b) in a circle of radius 8 meters is 4 N.
What is centripetal force?
Centripetal force can be defined as a necessary force acting of a body moving in circular or curved path in the direction of inwards towards a fixed point. Due to having both magnitude and direction, it is a vector quantity. SI unit of centripetal force is Newton (N).
We know that.
centripetal force = [tex]\frac{mv^{2} }{r}[/tex]
Where,
m = mass of the moving object.
v = speed of the moving object.
r = radius of the circular path.
Given,
Mass of the sack of flour = m= 2 kg.
Speed of the moving object = v = 4 m/s.
Now for condition (a),
When, radius of the circular path = r = 4 meter.
Required centripetal force = [tex]\frac{mv^{2} }{r}[/tex] = [tex]\frac{2*4*4}{4}[/tex] N = 8 N.
And, for condition (b),
When, radius of the circular path = r = 8 meter.
Required centripetal force = [tex]\frac{mv^{2} }{r}[/tex] = [tex]\frac{2*4*4}{8}[/tex] N = 4 N.
So, required centripetal force for conditions (a) and (b) respectively 8N and 4 N.
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